In neutrosophic topological space (NTS), the neutrosophic setting for regular generalized b-closed set is shown as a novel kind neutrosophic closed set (NCS). Moreover, several new ideas of (NCS) are given and discussed, like neutrosophic generalized preregular closed set, neutrosophic regular generalized α-closed set, neutrosophic generalized b-closed set set, neutrosophic generalized α-closed set , neutrosophic generalized semi pre-closed set, neutrosophic generalized αb-closed set, neutrosophic semi generalized b-closed set, in neutrosophic topological spaces. Moreover, the relationships between the neutrosophic regular generalized b-closed and these new classes in (NTS) are explained and studied their characters.
Some of the novel algebraic topics explored in this paper, like Permutation Q - algebra, permutation G - part, permutation p-radical, permutation p - semisimple and permutation ideal are discussed and looked into. We show that if ( X, #, {1}) is a permutation Q - algebra, then (λiβ # (λiβ # λjβ)) # λjβ = {1}, ∀λiβ, λjβ ∈ X. Also, in the permutation G - part G(X) of X, the left cancellation law is hold and for any β - set λiβ in Permutation Q - algebra (X, #, {1}), we consider that λiβ belongs to G(X). Additionally permutation implicative, homomorphism, kernel and image of permutation Q - algebras were defined with specific results relating to our unique notions have been developed and examined.
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